A068092
Index of smallest triangular number with n digits.
Original entry on oeis.org
1, 4, 14, 45, 141, 447, 1414, 4472, 14142, 44721, 141421, 447214, 1414214, 4472136, 14142136, 44721360, 141421356, 447213595, 1414213562, 4472135955, 14142135624, 44721359550, 141421356237, 447213595500, 1414213562373, 4472135955000, 14142135623731
Offset: 1
a(4) = 45 as the 45th triangular number is 45*46/2 = 1035 while the 44th is 990.
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[Round(Sqrt(2*10^(n-1))) : n in [1..30]]; // Vincenzo Librandi, Oct 05 2011
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f[n_] := Block[{a = Floor[Sqrt[2*10^n]]}, If[a(a + 1)/2 < 10^n, a++ ]; Return[a]]; Table[ f[n], {n, 0, 30} ]
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a(n) = round(sqrt(2*10^(n-1))) \\ Charles R Greathouse IV, Oct 04 2011
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from math import isqrt
def A068092(n): return isqrt(10**(n-1)<<3)+1>>1 # Chai Wah Wu, Oct 17 2022
A095864
Largest n-digit triangular number.
Original entry on oeis.org
6, 91, 990, 9870, 99681, 998991, 9997156, 99991011, 999961560, 9999878910, 99999957291, 999999911791, 9999997965180, 99999998250180, 999999997764120, 9999999895728690, 99999999552805215, 999999998765257141
Offset: 1
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Join[{6},(#(#+1))/2&/@Table[Floor[(Sqrt[8*10^n+1]-1)/2],{n,2,30}]] (* Harvey P. Dale, Jul 27 2012 *)
triInverse[n_] := Floor[(Sqrt[1 + 8*n] - 1)/2]; tri[n_] := n*(n+1)/2; Table[tri[triInverse[10^n - 1]], {n, 18}] (* T. D. Noe, Jul 27 2012 *)
A095866
Largest n-digit number - largest n-digit triangular number.
Original entry on oeis.org
3, 8, 9, 129, 318, 1008, 2843, 8988, 38439, 121089, 42708, 88208, 2034819, 1749819, 2235879, 104271309, 447194784, 1234742858, 2234186964, 3266133123, 22172578524, 114481278033, 204796672749, 841526085621, 355055477499
Offset: 1
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lndt[n_]:=Module[{c=Floor[(Sqrt[8*10^n+1]-1)/2]},(c(c+1))/2]; Join[{3}, Table[ 10^n-1-lndt[n],{n,2,30}]] (* Harvey P. Dale, May 16 2017 *)
A068093
Smallest n-digit triangular number.
Original entry on oeis.org
1, 10, 105, 1035, 10011, 100128, 1000405, 10001628, 100005153, 1000006281, 10000020331, 100000404505, 1000001326005, 10000002437316, 100000012392316, 1000000042485480, 10000000037150046, 100000000000018810, 1000000000179470703, 10000000002237948990
Offset: 1
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triInverse[n_] := Floor[(Sqrt[1 + 8*n] - 1)/2]; tri[n_] := n*(n+1)/2; Table[tri[1 + triInverse[10^(n-1) - 1]], {n, 20}] (* T. D. Noe, Jul 27 2012 *)
A095863
Index of largest triangular number with n digits.
Original entry on oeis.org
3, 13, 44, 140, 446, 1413, 4471, 14141, 44720, 141420, 447213, 1414213, 4472135, 14142135, 44721359, 141421355, 447213594, 1414213561, 4472135954, 14142135623, 44721359549, 141421356236, 447213595499, 1414213562372
Offset: 1
A095865
Smallest n-digit triangular number - smallest n-digit number.
Original entry on oeis.org
0, 0, 5, 35, 11, 128, 405, 1628, 5153, 6281, 20331, 404505, 1326005, 2437316, 12392316, 42485480, 37150046, 18810, 179470703, 2237948990, 10876002500, 22548781025, 26940078203, 242416922750, 572687476751, 4117080477500
Offset: 1
Showing 1-6 of 6 results.
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